Euler 23 在 C# 中：0.2 秒，在 F# 中：30.5 秒。为什么？

我对这个问题的 F# 解决方案不太满意，因为我找不到一个漂亮且快速的解决方案，但这不是这里的问题。问题是，我将解决方案翻译成 C#，而且速度很快。就像，相对而言，速度非常快。

我不明白为什么。是的，我去过 Reflector，C# 代码看起来很相似，不能说我真的理解 IL，但看起来有点像。我唯一能想到的是 F# int[] 相对于 C# List 的性能。

所以事情是这样的：

F#

module Euler023

let divisorsSum n =
  let mutable sum = 1
  let limit = (int (sqrt(float n)))
  for i in [2..limit] do
    if n%i=0 then sum <- sum+i+n/i
  if (limit*limit)=n then sum-limit else sum

let isAbundant x = (divisorsSum x)>x
let abundants  = [1..28123] |> List.filter isAbundant |> List.toArray
let domain = System.Collections.BitArray(28124)

let rec loopUntil i j =
    if i=abundants.Length then ()
    elif j=abundants.Length then loopUntil (i+1) (i+1)
    else
      let sum = abundants.[i]+abundants.[j] 
      if sum<28124 then 
        domain.Set(sum, true)
        loopUntil i (j+1)
      else 
        loopUntil (i+1) (i+1)

let solve  =    loopUntil 0 0
            [1..28123] |> List.filter (fun x -> domain.Get(x)=false) |> List.sum

C#

static int divisorsSum(int n)
{
    int sum = 0;
    var limit = (int)Math.Sqrt(n);

    for (int i=2;i<=limit;++i) if (n%i==0) sum += i + n/i;

    if ((limit * limit) == n) return sum-limit;

    return sum;
}

static List<int> getAbundants(int ceiling)
{
    var ret = new List<int>();

    for (int i = 1; i < ceiling; ++i) if (divisorsSum(i) > i) ret.Add(i);

    return ret;
}

 static void Main(string[] args)
 {

     var abundants = getAbundants(28124);
     var bitField = new bool[28124];

     for (int i = 0; i < abundants.Count; ++i)
         for (int j = i; j < abundants.Count; ++j)
         {
             var sum = abundants[i] + abundants[j];
             if (sum < 28124) bitField[sum] = true;
             else break;
         }

     var total = 0;
     for (int i = 0; i < 28124; ++i) if (bitField[i]==false) total += i;

}

Update

包含此代码的项目由每个问题的单独文件 (EulerXXX.fs) + 主程序文件组成。主程序文件如下

module Program =


let stopWatch = System.Diagnostics.Stopwatch()
let mutable totalTime = System.TimeSpan()

let inline tick()
 = 
    stopWatch.Stop();
    totalTime <- totalTime.Add stopWatch.Elapsed
    printfn " -> Elapsed: %2.2f sec Total: %2.2f s" stopWatch.Elapsed.TotalSeconds  totalTime.TotalSeconds
    stopWatch.Restart()

let _ = 

    stopWatch.Start()
    printf "Euler001 solution: %A" Euler001.solve
    tick()
    printf "Euler002 solution: %A" Euler002.solve
    tick()
    printf "Euler003 solution: %A" Euler003.solve
    tick()
    printf "Euler004 solution: %A" Euler004.solve
    tick()
    printf "Euler005 solution: %A" Euler005.solve
    tick()
    printf "Euler006 solution: %A" Euler006.solve
    tick()
    printf "Euler007 solution: %A" Euler007.solve
    tick()
    printf "Euler008 solution: %A" Euler008.solve
    tick()
    printf "Euler009 solution: %A" Euler009.solve
    tick()
    printf "Euler010 solution: %A" Euler010.solve
    tick()
    printf "Euler011 solution: %A" Euler011.solve
    tick()
    printf "Euler012 solution: %A" Euler012.solve
    tick()
    printf "Euler013 solution: %A" Euler013.solve
    tick()
    printf "Euler014 solution: %A" Euler014.solve
    tick()
    printf "Euler015 solution: %A" Euler015.solve
    tick()
    printf "Euler016 solution: %A" Euler016.solve
    tick()
    printf "Euler017 solution: %A" Euler017.solve
    tick()
    printf "Euler018 solution: %A" Euler018.solve
    tick()
    printf "Euler019 solution: %A" Euler019.solve
    tick()
    printf "Euler020 solution: %A" Euler020.solve
    tick()
    printf "Euler021 solution: %A" Euler021.solve
    tick()
    printf "Euler022 solution: %A" Euler022.solve
    tick()
    printf "Euler023 solution: %A" Euler023.solve
    tick()
    printf "Euler024 solution: %A" Euler024.solve
    tick()
    printf "Euler059 solution: %A" Euler059.solve
    tick()
    printf "Euler067 solution: %A" Euler067.solve
    tick()
    stopWatch.Stop()
    System.Console.ReadLine()

程序的输出如下：

Euler001 solution: 233168 -> Elapsed: 0.02 sec Total: 0.02 s
Euler002 solution: 4613732 -> Elapsed: 0.03 sec Total: 0.04 s
...
Euler022 solution: 871198282 -> Elapsed: 0.02 sec Total: 4.11 s
Euler023 solution: 4179871 -> Elapsed: 81.11 sec Total: 85.22 s
Euler024 solution: [2; 7; 8; 3; 9; 1; 5; 4; 6; 0] -> Elapsed: 0.01 sec Total: 85.23 s
...
Euler067 solution: [7273] -> Elapsed: 0.01 sec Total: 85.31 s

所以问题不在于项目参数。另外，如果我将代码从 Euler023 复制到 Program ，它将立即运行。 问题是，为什么只有这个问题才会出现这种放缓？

你的 F# 版本一点也不慢；在我的机器上，F# Interactive 需要 0.44 秒。我不知道你怎么能观察到这么慢（30.5 秒）。如果编译并运行代码，请确保处于发布模式并打开优化和尾调用消除。

但是，您仍然可以通过消除冗余中间集合的使用来进一步优化。

A. 变更（冗余）清单[2..limit]范围表达式2..limit in divisorsSum:

for i in 2..limit do
    if n%i=0 then sum <- sum+i+n/i

B. 生成丰度数组而不创建大列表（更忠实于 C# 版本）：

let abundants = 
    let arr = ResizeArray(28123)
    for i in 1..28123 do
        if isAbundant i then arr.Add i
    arr.ToArray()

C、计算solve无需创建大列表：

let solve = 
    loopUntil 0 0
    let mutable sum = 0
    for i in 1..28123 do
       if not <| domain.Get(i) then
            sum <- sum + i
    sum

新的 F# 版本比原始版本快 4 倍；大约需要0.1秒才能完成。

UPDATE:

你的测量不准确。首先，您测量了两次打印值调用之间的时间差。第二，EulerXXX.solve是价值观；因此它们是在编译程序时预先计算的。你应该声明EulerXXX.solve作为函数：

let solve() = ...

并测量函数调用的执行时间：

let time fn =
    let sw = new System.Diagnostics.Stopwatch()
    sw.Start()
    let f = fn()
    sw.Stop()
    printfn "Time taken: %.2f s" <| (float sw.ElapsedMilliseconds)/1000.0
    f

let s023 = time Euler023.solve
printf "Euler023 solution: %A" s023